This invention relates to a vibration damping equipment for damping the vibration of a structure due to an external force such as an earthquake and the wind.
Vibration damping equipment which includes a control device for damping a vibration mounted to a structure such as a high- and medium-rise building, and which receives energy supplied from the outside to damp positively a vibration is known by, for example, Tokkai Sho 63-217075 published in 1988 by the Japanese Patent Office. The equipment is such that, as shown in FIGS. 6 and 7, a mass 2 is supported in movable relationship by wheels 10 on a structure 1, and the mass 2 is allowed to be displaced by the use of hydraulic cylinders 6.
The mass 2 is connected in four horizontal directions with the four hydraulic cylinders 6. A rod 7 of each hydraulic cylinder 6 is connected at one end thereof to a wall 8 provided on the structure 1 in a manner to surround the mass 2, and is extended or retracted by a high-pressure hydraulic off supplied from a hydraulic unit 9 to drive the mass 2.
For example, if the structure is shaken in an any direction by an external force, the hydraulic cylinder 6 will drive the mass 2 in the same direction as that direction. This driving causes the force exerted on the structure 1 by the mass 2 to become opposite in direction to the external force acting on the structure 1, thereby providing an action of damping shaking of the structure 1. In this manner, the shaking of the structure due to an external force such as an earthquake and the wind is damped.
The structure 1 and the mass 2 are mounted with displacement sensors 11 and 12 for detecting an absolute displacement of the structure 1 and the mass 2, respectively.
FIG. 8 shows a control model for the equipment of FIGS. 6 and 7. In this model, for simplicity, one cylinder 6 is adapted to drive the mass 2. Now, it is assumed that where the mass 2 is shaken in a horizontal direction in FIG. 6, the mass 2 is shaken in a vertical direction in the model of FIG. 8.
The displacement sensor 11 detects an absolute displacement x.sub.1 of the structure 1, while the displacement sensor 12 detects an absolute displacement x.sub.2 of the mass 2.
The absolute displacements x.sub.1 and x.sub.2 exhibit a positive or negative value with the displacements taken as zero where the structure 1 and the mass 2 are positioned at their respective central position.
Signals from these displacement sensors 11 and 12 are inputted into a controller 30 comprising a state variable setting unit 31 and a calculation unit 32.
In the state variable setting unit 31, a relative displacement x.sub.2 ' of the structure 1 to the mass 2 is calculated by a subtracter 33 from the absolute displacements x.sub.1 and x.sub.2 of the structure 1 and the mass 2, and then in differentiators S1 and S2, from the relative displacement x.sub.2 ' and the absolute displacement x.sub.1, an absolute velocity v.sub.1 of the structure 1 and a relative velocity v.sub.2 ' of the structure 1 to the mass 2 are calculated.
The state variables (the absolute displacement x.sub.1, the absolute velocity v.sub.1, the relative displacement x.sub.2 ' , the relative velocity v.sub.2 ') thus calculated are inputted into the calculation unit 32. In the calculation unit 32, each state variable is multiplied by an optimum preset feedback gain matrix K=(f.sub.1 f.sub.2 f.sub.3 f.sub.4), and a control input value u obtained by adding these multiplied values is calculated by the following EQU u=f.sub.1 *x.sub.1 +f.sub.2 *x.sub.2 '+f.sub.3 *v.sub.1 +f.sub.4 *v.sub.2 'Equation 1
The optimum feedback gain matrix K is preset so that the evaluation function becomes minimum on the basis of an optimum regulator theory. The method of calculating the optimum feedback gain matrix K and the evaluation function on the basis of an optimum regulator theory is well known and disclosed in the following document:
"A Guide to System Control Theory" (by K. Ogo and T. Mita, published by Jikkyo Shuppan Co., pp. 157-160, Dec. 15, 1979)
The optimum regulator theory will be briefly explained. A vibration exciting force exerted on the structure 1 is taken as F, and a state variable x=(x.sub.1 x.sub.2 ' v.sub.1 v.sub.2 ').sup.T. By the use of these, linearizing properly a physical equation representing the model of FIG. 8 causes the following equations to be obtained: EQU x=A*x+B*u+E*F Equation 2 EQU y=C*x Equation 3
In the above-mentioned equations, A, B and E are constant matrixes of 4.times.4, 4.times.1 and 4.times.1, respectively, determined by the items of the structure 1 and a vibration damping equipment; and C is a constant matrix of n.times.4 (in this case, 4.times.4) determined according to the number of state variables inputted. At this point, the feedback gain matrix K is calculated by the following equation using the matrixes A and B in the equation 2: EQU K=R.sub.K.sup.-1 *B.sup.T *P.sub.K Equation 4
where, P.sub.K is a solution to a matrix equation shown in Equation 5: EQU P.sub.K *A+A.sup.T *P.sub.K -P.sub.K *B*R.sub.K.sup.-1 *B.sup.T *P.sub.K +Q.sub.K =0 Equation 5
where, Q.sub.K and R.sub.K are design parameters.
The control input value u outputted from the controller 30 on the basis of the optimal feedback gain matrix K thus calculated is conducted to a solenoid 15 for driving a spool 14 of a servo valve 13.
In FIG. 8, of three upper ports of the servo valve 13, a central port 16 communicates with a pump P, and right and left ports 17 and 18 communicate with a tank T. The two lower ports 19 and 20 communicate with oil chambers of the hydraulic cylinder 6.
In FIG. 8, when the structure 1 receives an external force such as an earthquake and the wind and begins to shake in the upper direction in FIG. 8 (equivalent to right direction in FIG. 6), the controller 30 calculates the control input value u from signals detected in the displacement sensors 11 and 12.
The control input value u is outputted to the solenoid 15 to cause the spool 14 of the servo valve 13 to be displaced to the right position as shown in FIG. 8. In this state, a hydraulic off is supplied through the ports 13 and 20 to the lower oil chamber of the cylinder 6, while the hydraulic oil of the upper oil chamber is returned through the ports 19 and 18 to the tank T, whereby the piston is pushed up in the cylinder 6.
That is, the rod 7 of the hydraulic cylinder 6 causes the mass 2 to be displaced behind in the movement of the structure 1 in the upward direction as with the structure 1. Conversely when the structure 1 is shaken in the downward direction, the sign of the control input u becomes opposite, so that the spool 14 is slid in the left direction of FIG. 8 to cause the mass 2 to be driven downward.
A reaction force developed by moving the mass 2 acts on the structure 1 against the external force exerted on the structure 1. The reaction force causes the vibration on of the structure 1 to be damped.
In the vibration damping equipment, its control system has been simplified by neglecting a high-order vibration mode equal to or higher than two-order, and the control gain set on the basis of the optimal feedback theory has been made a constant value without according to a vibration frequency as shown in FIG. 9. Therefore, increasing the control gain to improve the vibration effect of a structure may have caused a vibration due to the neglected high-order vibration mode or a vibration due to the response characteristics of the servo valve and to the compressibility of the hydraulic oil to be developed in the structure.
Since the control gain is a constant value, a disturbance with a very long cycle due to the wind is exerted on a structure, a problem has existed in that the mass is displaced excessively as shown in FIG. 10, whereby the effective stroke of the hydraulic cylinder used to damp a disturbance with a short cycle due to an earthquake is reduced by the excessively displaced portion.
Further, it is necessary to give all four state variables required for control to the equipment, so that the configuration of devices such as differentiator for performing the signal processing of sensors has become complex, thereby partly causing the manufacturing cost of the equipment to be increased.